fa.m

clc;
clear;
close all;

%% Problem Definition

CostFunction=@(x) Rosenbrock(x);        % Cost Function

nVar=2;                 % Number of Decision Variables

VarSize=[1 nVar];       % Decision Variables Matrix Size

VarMin=-10;             % Decision Variables Lower Bound
VarMax= 10;             % Decision Variables Upper Bound

%% Firefly Algorithm Parameters

MaxIt=10;         % Maximum Number of Iterations

nPop=10;            % Number of Fireflies (Swarm Size)

gamma=1;            % Light Absorption Coefficient

beta0=1;            % Attraction Coefficient Base Value

alpha=0.01;          % Mutation Coefficient

alpha_damp=0.98;    % Mutation Coefficient Damping Ratio

delta=0.05*(VarMax-VarMin);     % Uniform Mutation Range

m=2;

if isscalar(VarMin) && isscalar(VarMax)
    dmax = (VarMax-VarMin)*sqrt(nVar);
else
    dmax = norm(VarMax-VarMin);
end

%% Initialization

% Empty Firefly Structure
firefly.Position=[];
firefly.Cost=[];

% Initialize Population Array
pop=repmat(firefly,nPop,1);

% Initialize Best Solution Ever Found
BestSol.Cost=inf;

% Create Initial Fireflies
for i=1:nPop
   pop(i).Position=unifrnd(VarMin,VarMax,VarSize);
   pop(i).Cost=CostFunction(pop(i).Position);
   
   if pop(i).Cost<=BestSol.Cost
       BestSol=pop(i);
   end
end

% Array to Hold Best Cost Values
BestCost=zeros(MaxIt,1);

%% Firefly Algorithm Main Loop

for it=1:MaxIt
    
    newpop=repmat(firefly,nPop,1);
    for i=1:nPop
        newpop(i).Cost = inf;
        for j=1:nPop
            if pop(j).Cost < pop(i).Cost
                rij=norm(pop(i).Position-pop(j).Position)/dmax;
                beta=beta0*exp(-gamma*rij^m);
                e=delta*unifrnd(-1,+1,VarSize);
                %e=delta*randn(VarSize);
                
                newsol.Position = pop(i).Position ...
                                + beta*rand(VarSize).*(pop(j).Position-pop(i).Position) ...
                                + alpha*e;
                
                newsol.Position=max(newsol.Position,VarMin);
                newsol.Position=min(newsol.Position,VarMax);
                
                newsol.Cost=CostFunction(newsol.Position);
                
                if newsol.Cost <= newpop(i).Cost
                    newpop(i) = newsol;
                    if newpop(i).Cost<=BestSol.Cost
                        BestSol=newpop(i);
                    end
                end
                
            end
        end
    end
    
    % Merge
    pop=[pop
         newpop];  %#ok
    
    % Sort
    [~, SortOrder]=sort([pop.Cost]);
    pop=pop(SortOrder);
    
    % Truncate
    pop=pop(1:nPop);
    
    % Store Best Cost Ever Found
    BestCost(it)=BestSol.Cost;
    
    % Show Iteration Information
    disp(['Iteration ' num2str(it) ': Best Cost = ' num2str(BestCost(it))]);
    
    % Damp Mutation Coefficient
    alpha = alpha*alpha_damp;
    
end